Anti-cancer treatment schedule optimization based on tumor dynamics modelling incorporating evolving resistance

Quantitative characterization of evolving tumor resistance under targeted treatment could help identify novel treatment schedules, which may improve the outcome of anti-cancer treatment. In this study, a mathematical model which considers various clonal populations and evolving treatment resistance was developed. With parameter values fitted to the data or informed by literature data, the model could capture previously reported tumor burden dynamics and mutant KRAS levels in circulating tumor DNA (ctDNA) of patients with metastatic colorectal cancer treated with panitumumab. Treatment schedules, including a continuous schedule, intermittent schedules incorporating treatment holidays, and adaptive schedules guided by ctDNA measurements were evaluated using simulations. Compared with the continuous regimen, the simulated intermittent regimen which consisted of 8-week treatment and 4-week suspension prolonged median progression-free survival (PFS) of the simulated population from 36 to 44 weeks. The median time period in which the tumor size stayed below the baseline level (TTS<TS0) was prolonged from 52 to 60 weeks. Extending the treatment holiday resulted in inferior outcomes. The simulated adaptive regimens showed to further prolong median PFS to 56–64 weeks and TTS<TS0 to 114–132 weeks under different treatment designs. A prospective clinical study is required to validate the results and to confirm the added value of the suggested schedules.


Contents
. When fixing kM2 and kM4 to zero, the simulated time-curves of total tumor burden and each clonal population (a,d,g), mutation concentrations (b,e,h), and dosing strategies (c,f,i) of a typical subject with metastatic colorectal cancer undergoing continuous treatment (a,b,c), intermittent treatment (8-week treatment and 4-week suspension) (d,e,f), and adaptive treatment with the second hypothetical drug (ctDNA limits for drug adjustment: 5 and 10 fragments/ml, monitor frequency: 12 weeks) (g,h,i

Parameter estimate
To assist the setting of parameter values, the values of parameter describing tumor dynamics under anti-EGFR inhibitor ( ! ) therapy were estimated by fitting the collected tumor sizes data 1 using the first order conditional estimation method with interaction (FOCEI) implemented in NONMEM software, version 7.4.1 (ICON Development Solutions).
A non-linear mixed-effect model was developed. Parameters were assumed to be lognormally distributed and were expressed using equation (S1). " represents the parameter of th individual, #$# represents typical value of the parameter, and " represents the random inter-individual variability (IIV) which was normally distributed with mean of 0 and variance of % . The residual error was characterized with a proportional error model as is shown in equation (S2), where represents observations, represents individual predictions, and ! represents the proportional residual error which was assumed to be normally distributed with mean of 0 and variance of ! % .
'% , as was assumed, was fixed as 0.021 /week (0.03•70%). The baseline levels of and mutant KRAS ( ()*+,! ) were fixed according to real observations of each patient. For WT-KRAS patients, the baseline of -! were set to 0. For M-KRAS patients, the baseline of -! was estimated and the baseline of . equals the difference between the observed baseline and estimated baseline -! .

Model in a evaluation cohort
The model used in the evaluation cohort was adjusted according to the findings of the study: 1) The detectable EGFR L858R mutation or exon 19 deletion in ctDNA at the start of treatment indicates the tumor is sensitive to anti-EGFR inhibitor. Therefore, the sensitive clonal population ( " ) was assumed to carry one of these two mutations ( #$%&'! ); 2) L858R mutation or exon 19 deletion became undetectable when EGFR inhibitor ( ! ) started and raised back again together with the newly developed EGFR T790M mutation ( #$%&'( ) during treatment 3 , which indicates the emergence of treatment resistance. Therefore the acquired resistant clonal population under ! ( )! ) was assumed to carry both ()*+,! and ()*+,% ; 3) A hypothetical treatment next to anti-EGFR inhibitor ( ( ) was incorporated and assumed to target T790M positive NSCLC cancer ( )! ). In the meantime, a third mutation (  3 ) was able to be acquired which resulted in a third clonal population ( )( ) that were resistant to ( . More details of the model and the parameters are shown in Supplementary Fig. S1 and Supplementary Table S6.
The values of parameters regarding tumor dynamics were estimated using the collected time curves of tumor sizes as described above. The residual error was characterized with an additive error model as is shown in equation S3, where represents observations, represents individual predictions, and ( represents the additive residual error which was assumed to be normally distributed with mean of 0 and variance of % % . The parameter estimate results can be found in Supplementary Table S7.

Figure S1
The model structure that characterize the dynamics of tumor size and mutation concentrations in ctDNA from NSCLC patients.